EXAMPLES OF UNDETERMINED SCATTERING PROBLEMS

The determination of the shape of a scatterer by non-destructive metho ds, such as scattering experiments, raises the question of indetermina tion or ambiguity problems for the scatterer's shape, depending on the given scattering data. These ambiguity problems are discussed here by means of numerical constructions of equivalent scattering problems, i .e. we determined scatterers that produced the same scattering amplitu de in given conditions (fixed energies, fixed incident angles and/or d irections of receivers). This construction is given in the context of a generalized scattering theory that takes into account impedance disc ontinuities inside the scatterer. We started with a scattering problem defined by a discontinuous curve of arbitrary shape and defined by bo undary conditions. Then, a circular curve with appropriate boundary co nditions was determined such that these two scattering problems yielde d the same scattering amplitude within the given conditions. We also p resent numerical results for two particular cases of the generalized s cattering theory, calculated by means of the Nystrom method. We used t hese results to verify that the equivalence obtained in the Born appro ximation holds for the exact scattering amplitudes.